Hi,
I don't expect longer livetime with a 18650 battery due to it's chemistry livetime and self discharge.
Coin battery: as long as the system is mains powered there shoukd be no current drain from V_bat.
Thus the coin cell need only deliver power when mains is off.
How long is the longest expectable main off period? Maybe a goldcap as an alternative.
There is a charger. What is the expectable peak (!!) voltage at the battery? Are you sure this is within STM32 specification?
To minimize capacitor leakage current you may use a ceramics capacitor with much higher voltage rating, or use a foil capacitor...and for sure a PCB and layout with low leakage current, maybe the PCB needs to be carefully cleaned after solder process.
Klaus